On the Embedding Waterman, Chanturia and Generalized
Wiener Classes in the Classes $H_{1}^{\omega}$

abstract:
Chanturia, Wang and Akhobadze proved sufficient conditions for the inclusion of
Chanturia, Waterman and Generalized Wiener classes, respectively, in the classes
$H_{1}^{\omega }$. In this paper we prove that these conditions are necessary
for this inclusion to hold.